A Research On Dimension Folding Reduction Method Based On Longitudinal Data And Its Case Study

In recent years,with the application of big data gradually integrated into people's life,the dimension reduction method that can retain the internal structure of data has gradually attracted more and more attention,especially in the longitudinal data with a wide range of needs.This paper will mainly discuss the dimensionfolding reduction method of longitudinal structural data and its effective application in the field of practical medical diseases.In this paper,the dimension folding principal component analysis method is proposed to reduce the dimension of longitudinal data.This method can reduce the dimension of variables and time while preserving the inherent structure of the original data without destroying the correlation of it.Specifically,for the original longitudinal data,it is regarded as matrix value data and then maximum likelihood estimation method is used to estimate the folded subspace of the central dimension in the horizontal and vertical direction,so as to achieve dimension reduction in two dimensions respectively and retain the original structure of the data.Furthermore,through simulation experiments,the longitudinal data under two data-related conditions is considered :(1)The data with the isotropic error;(2)The data with the general error.Comparing the proposed dimension folding principal component analysis method with the traditional principal component analysis method,the simulation results show that the proposed method has a smaller estimation error with two kinds of longitudinal data considered,so the effectiveness of the proposed method is verified numerically.Further on,this paper will offer the dimension folding principal component analysis on primary biliary cirrhosis disease data to predict the survival of patients.Based on the reduction of dimension reduction direction to low dimensional projection data,and establish the nonparametric model to predict survival,with the traditional linear mixed effects model prediction effect comparison,the results show that the proposed method on non-parametric modeling with smaller prediction error,reflected the proposed dimension reduction method in the analysis of longitudinal rationality and superiority.